Workpiece shape control

ABSTRACT

A method of controlling the shape of a workpiece in a singlestand, multipass rolling mill when the final gage and crown are specified. The roll-separating force required on each reducing pass is calculated as a function of (1) roll elasticity, diameter, and crown and (2) workpiece crown, resistance to deformation, and width. The per unit target crown for each pass n is calculated by multiplying the per unit target crown for pass n+1 (using the final per unit crown as the first pass n+1 per unit target crown) by a crown-slope multiplier greater than one. The multiplier is a function of final width and final gage and is subject to change in response to observations of the shapes of previously rolled workpieces. Also disclosed is pattern control through adjustment of rolling force levels.

United States Patent 9 Claims, 17 Drawing Figs.

3,474,668 l0/1969 Mangan Primary ExaminerMilton S. Mehr Att0rneys-lohn B, Sponsler, Gerald R. Woods, James C.

Davis, Jr., Frank L. Neuhauser, Oscar B. Waddell and Arnold E. Renner ABSTRACT: A method of controlling the shape of a workpiece in a single-stand, multipass rolling mill when the final gage and crown are specified. The roll-separating force required on each reducing pass is calculated as a function of [52] U.S. Cl 72/6, (1) roll elasticity, diameter, and crown and (2) workpiece 72/19 crown. resistance to deformation, and width. The per unit tar- [51] Int. Cl. B2lb 37/00 get crown for each pass n is calculated by multiplying the per [50] Field of Search 72/8, 16, 21 unit target crown for pass n+1 (using the final per unit crown as the first pass n+1 per unit target crown) by a crown-slope [56] Relerences C'led multiplier greater than one. The multiplier is a function of UNITED STATES PATENTS final width and final gage and is subject to change in response 3 24 91 5/1966 Kenyon at 72/16 X to observations of the shapes of previously rolled workpieces. 3 31 24 5 19 7 plaisted 72/ Also disclosed is pattern control through adjustment of rolling 3,387,470 6/1968 Smith, Jr. 72 7 force levels- 3,394,566 7/1968 O'Brien 72/21 X 5 l l G AUXILIARY INPUT COMPUTER scRewDowN X CONTROL l6 2 SCREWDOWN CONTROL 22 41 20 LOAD g 5 CELL PATTERN PLATE n-ncrmess f'lONlTOR TRACKING GAGE L9 48 A I n 26 J l4- FLATNESS HONlTOR msmznmnzm v 3330.055

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1 WORKPIECE SIIAPE CONTROL v BACKGROUND OF THE INVENTION The present invention relates to the reduction of a workpiece in a rolling mill and more particularly to methods for controlling the shape of a workpiece or plate being reduced in the rolling mill.

In a plate-rolling mill, a heated plate passes between a pair of rotating work rolls forming an unloaded opening smaller than the entry gage of the plate. The passage of the plate between the rolls results both in a reduction in plate thickness and a bending of the rolls. The rolls, being confined at their ends, separate more at their middles when bent by the rollseparating forces. Consequently, the gage or thickness along the centerline of the delivered plate is normally somewhat greater than at the edges. The difference between the gage along the centerline and the gage at the edges of a plate is referred to as the crown on the plate. Where the center gage is thicker than the edge gage, the crown is termed positive. Where the center gage is thinner, the crown is termed negative. The magnitude of crown formed on a plate is determined by the amount of bending of the rolls and by the shape of the rolls themselves. The bending of the rolls is partly a junction of roll-separating force which, in turn, varies with the magnitude of the draft (reduction in gage) taken during a pass. The shape or effective crown of the rolls is determined by their initial shape as altered due to thermal expansion and wear. New rolls are normally ground with a positive crown to partially offset the effects of roll-bending, thereby preventing the formation of excessive crowns on plates. The ground crown increases once rolling begins due to a thermally induced roll crown which results from unequal thermal expansion along the surface or face of the roll. As the rolls wear from continued use, the total or effective crown diminishes due to the unequal wear pattern across the face of the roll.

Although it is possible to roll a plate with perfectly flat, parallel surfaces by bending the rolls just enough to offset the effective roll crown, it is normally more desirable to roll a plate having some positive crown. Rolls bent sufficiently to form a positive crown on a plate tend to center the plate in the mill by forcing it into the area of the greatest roll separation, which is at the middle of the rolls. Moreover, the greater drafts and higher roll-separating forces which lead to the formation of positive plate crowns also lead to increased productivity by reducing the number of passes needed to reduce a plate from a given initial gage to a desired final gage. There is, however, a limit on the amount of positive crown that is desirable on a plate. In ordering metal plate, a customer usually specifies an overweight limit for plates of given material, length, width, and edge gage. Since plate overweight is due to the material in the crowned sections of the plate, the overweight limit effectively limits permissible crown.

Plate crown control is one aspect of plate shape control. Other aspects differ depending on whether the plate is in a roughing phase or a finishing phase. During the roughing phase, a slab is delivered to a roughing mill from a slab supply area. Initial reductions in thickness are taken, and the width of the finished plate is established by elongating the slab length to the desired plate width in cross-rolling passes.

The formation of a plate crown, whether positive or negative, may be accompanied by unequal elongation of the slab or plate across its width. Unless the unequal elongation is cancelled out by compensating elongation before or during the last pass, the pattern or plan view of the slab will not be rectangular, but will include concave or convex ends. Because a slab is turned 90 before being rolled in the finishing phase, a finished plate rolled from such a slab will not be rectangular but will similarly have concave or convex edges. Plate edges are trimmed to a straight line leading to a yield loss or waste of materials for nonrectangular plates. The control of slab configuration during a roughing phase to produce a more nearly rectangular slab is referred to as pattern control, a second aspect of shape control during the roughing phase.

During the finishing phase of plate rolling, crown control and flatness control are related aspects of shape control. The flatness of a plate is a measure of the deviation of the plate surfaces from a planar surface. Although plate flatness can be improved by operations following the rolling process, it is primarily established during the finishing phase of the rolling process. Flatness is related to changes in the per unit crown (or ratio of crown to edge gage) which occur after the plate becomes too rigid to accommodate the unequal elongations accompanying crown formation. If the per unit crown is increased too abruptly, the material at the edges of the plate is elongated considerably more than the material along the centerline, which can result in wavy edges on the plate. Conversely, if the per unit crown is reduced too abruptly, the material along the centerline of the plate is elongated considerably more than the material along the edges, which may result in the plate having a buckled area along its centerline. Naturally, a plate having wavy edges or a buckled center will seldom be suited for an ultimate use until it is processed to eliminate the distortions.

Until recently, shape control was strictly a manual operation in which operators attempted to set roll openings in complete reliance on their experiences in rolling plates of similar initial and final dimensions and similar composition under similar conditions of temperature and roll size and crown. While a skilled operator may do an excellent job of controlling the shape of a plate, such skill is developed only after years of practice which are usually costly in terms of wasted material and wasted production time.

Automatic control of plate shape been attempted by a control system which calculates and controls the successive roll openings in a single-stand, multipass rolling mill in such a way that the per unit crown on a plate is maintained at a constant value during the last few passes of the plate through the mill. When the per unit crown remains constant, the area along the centerline of the plate is elongated the same amount as the area at the edges and the plate should be flat when finally delivered from the rolling mill. While this method of controlling shape could be effective, it may take longer to perform than is desirable. Maintaining the per unit crown at a constant value may require extra passes or the scheduling of drafts less than the maximumdraft which would be allowable while maintaining flatness.

SUMMARY OF THE INVENTION The present invention recognizes that plate crown is a function of mill and plate dimensions, rolling force, and plate resistance to deformation. It also recognizes that plate flatness is not totally dependent on plate crown, but may be modified independently of the final plate crown by altering the relationship between per unit plate crowns on successive passes. In accordance with the present invention, a target crown is selected during the finishing phase based upon the final width and gage of the plate. The force required on the last pass to form the target crown is then established as a function of the crown, diameter, and modulus of elasticity of the rolls, and of the width and resistance to deformation of the plate. The crowns on earlier passes are determined as a function of final plate crown, plate width and plate resistance to deformation whereas the forces required to produce these crowns are calculated as outlined above. The drafts and gages are established from the plates resistance to deformation. The stretch or distortion of the mill is determined for each rolling pass at the predicted force level. The rolls are positioned prior to each pass according to the predicted stretch, entry gage, and delivery gage. The plate is then passed between the positioned rolls.

The present invention further recognizes that a definite relationship exists between plate pattern during the roughing phase and the force calculations outlined above. The invention includes the calculation of forces needed to bend the rolls sufficiently to improve plate pattern.

DESCRIPTION OF THE DRAWINGS While the specification concludes with claims particularly pointing out and distinctly claiming that which is regarded as the present invention, the details of a preferred form of the invention may be more readily ascertained from the following detailed description when read in conjunction with the accompanying drawings in which:

FIG. 1 is a block diagram of the environment and the elements needed to practice the present invention;

FIG. 2, consisting of FIGS. 2A and 28, illustrates the effects of workpiece width on roll deflection;

FIGS. 3 and 4 are graphs of the effects of workpiece width on force multipliers appearing in a crown-force equation; and

FIG. 5 is a graph of a plate-deformation curve relating rollseparating force to expected drafts;

FIG. 6 is a graph relating deformation resistances at various plate widths to a force multiplier MI-l;

FIG. 7 is a plan view of a slab with an undesirable pattern;

FIG. 8 shows one embodiment of a slab pattern monitor;

FIG. 9, consisting of FIGS. 9A and 98, represents the rollplate interface for soft and hard plates;

FIG. 10 includes exaggerated cross-sectional views of the same plate on three successive passes during a finishing phase;

FIG. 1 l is a graph of typical per unit crown values, absolute crown values, and gage values occurring during a rolling schedule generated in accordance with the methods of the present invention;

FIG. 12 is a plan view of one embodiment of a plate-flatness monitor; and

FIG. 13 is a side view of the monitor shown in FIG. 12.

DETAILED DESCRIPTION Referring now to FIG. 1, the process of reducing a short, thick metal slab to a much longer and much thinner finished metal plate is normally carried out in two successive phases. During the first or roughing phase, the heated slab may be reduced to a desired gage and a desired length by passing it back and forth through a roughing mill 10 consisting of a pair of reversibly driven work rolls 12 and 14. The distance between adjacent faces of the work rolls 12 and 14 is reduced between succeeding passes by a screwdown mechanism including a screwdown control 16 which controls the angular position of a screw 18 threaded through an anchored nut (not shown) in the housing for the roughing mill 10. The rollseparating forces produced by the passage of a slab between the work rolls 12 and 14 are monitored by a load cell 20 interposed between the lower end of the screw 18 and the end support for the work roll 12. Although a single screw 18 is shown, it should be understood that an identical screw is located above the opposite end support for the work roll 12.

The objective of the roughing phase is to produce a slab of predetermined length and rectangular configuration or pattern when viewed from above. In the roughing mill, the slab pattern is monitored by an element referred to as a pattern monitor 22. In practice, the function of monitoring the pattern of a slab is generally performed by a mill operator for economic reasons although a mechanism such as is described later may be used.

Upon completion of the roughing phase the slab may be turned 90 before delivery to a finishing mill 24 located along a mill table 26. During a finishing phase, the slab (not termed a plate") passes back and forth between a pair of reversibly driven work rolls 28 and 30 in the finishing mill 24. The finishing mill 24 may he a four-high mill in which the work rolls 28 and 30 are backed by larger backup rolls 32 and 34, respectively. As in the roughing mill, the relative positions of the work rolls 28 and 30 are controlled by a screwdown mechanism including a screwdown control 36 which controls the angular position of a screw 38 threaded through an anchored nut in the housing for the finishing mill 24. A second screw (not shown) also exists in the finishing mill at the opposite end of the backup roll 32. A finishing mill such as mill 24 normally differs from a roughing mill such as mill 10 in its inclusion of the backup rolls 32 and 34 which serve to distribute the screwdown forces exerted by the screws along the face of the work rolls 28 and 30. Roll-separating forces caused by the passage of back and forth between the work rolls 28 and 30 are monitored by a load cell 40 interposed between the screw 38 and one end support on backuproll 32.

It is possible to use the same mill for roughing and finishing purposes. For this reason, the rolling operations are described generally in terms of roughing and finishing phases. These phases may be carried out in a single roughing and finishing mill or a separate roughing mill and a separate finishing mill. The present invention is equally applicable to either arrangement.

The center and edge gage of a finished plate produced by a series of passes (referred to as a rolling schedule) is determined by thickness gage 42. The gage 42 may have separate gaging mechanisms located above the centerline and the edges of the finished plate or a single traversing gage which scans across the plate transversely to the direction of travel. A mechanical device, designated a flatness monitor 44, may determine whether the finished plate is perfectly flat, has wavy edges, or has a buckled center area. Such a device is described later. As a practical matter, however, an operator normally observes plate flatness and submits encoded observations indicating which of the three flatness conditions exists. The encoded observations are supplied to a computer 46 which also accepts signals from the load cells 20 and 40, the pattern monitor 22, and the thickness gage 42. Other inputs to the computer 46 are from a plate-tracking system 48 which determines the position of a plate within the mill by means of hot metal detectors or similar sensors and an auxiliary input 50 through which data is supplied as to initial and final dimensions, the composition, and the temperature of the plate at the beginning of the roughing phase. Data on roll diameters and on the crowns of newly installed rolls may also be supplied through auxiliary input 50.

While the computer 46 receives several input signals representing the end results of shape control in both the roughing mill 10 and the finishing mill 24, it provides only two output signals for effecting that shape control. The first of these output signals is applied to the screwdown control 16 to adjust the angular position of the screw 18 and thus the relative position of the work rolls 12 and 14 in the roughing mill 10. The second of the signals is applied to the screwdown control 36 which adjusts the relative position of the work rolls 28 and 30 in the finishing mill 24.

As one step in determining the proper roll opening for establishing a particular crown during a particular pass, it is necessary to determine the roll-separating force which will produce that crown. A crown force equation which may be used in carrying out crown control in either the roughing mill 10 or the finishing mill 24 is as follows:

In this equation, RM is proportional to the modulus of elasticity of the rolls, RD is proportional to the diameter of the rolls, MH is proportional to the resistance to deformation of the plate, PCW and RCW are proportional to the width of the plate, TC is proportional to the target crown on the plate, and ERC is proportional to the effective crown on the rolls. Of the terms listed above, the roll-modulus term RM, the roll-diameter term RD, and the effective roll crown term ERC represent mill characteristics whereas the resistance to deformation term MH, the plate width terms PC W and RC W, and the target workpiece crown term TC represent plate characteristics.

The magnitude of the roll-modulus term RM is a function of the effective modulus of elasticity of the rolls and is initially established as a function of the metallurgical composition of the rolls. The value of the term is, however, preferably not fixed. If the measured crowns on rolled plates following either the roughing or the finishing phase differ consistently from the predicted crowns at all plate widths and thicknesses, at least one term in the crown force equation must be adjusted to eliminate these consistent errors. Since roll deflection and consequently plate crown are directly related to roll modulus, the value of the term RM can be adjustable for this purpose.

The roll diameter term RD reflects changes in roll-separating forces required to compensate for changes in roll diameters following replacement of worn rolls by new rolls of different diameters. For a four-high mill such as finishing mill 24, separate roll-diameter terms can exist for each of the work rolls 28 and 30 and for each of their respective backup rolls 32 and 34. If the range of roll diameters is small, a linear approximation can be used to derive the roll-diameter term RD from the actual magnitude of the diameters. For either the work rolls or the backup rolls, the linear approximation would be RD=131 k(D,,D,,) where k is a predetermined constant multiplier, D is a base diameter for the roll, and D is the actual diameter of the roll. The multiplier k in this equation is established theoretically and verified by observations. In a particular mill, k was found to be on the order of 0.05. When an average roll-diameter term for the work rolls and an average roll-diameter term for the backup rolls have been obtained, the two terms may be multiplied to provide a single term for use in the force equation.

Where the range of roll diameters is large as it may be in a two-high mill such as roughing mill 10, the linear approximation can not be used. Instead, roll-diameter term values obtained from theory and observations may be stored as a function of specific roll diameters in memory units in computer 46. The proper roll-diameter diameter term is found merely by entering the memory units through auxiliary input 50 with the actual roll diameters to extract the corresponding term values for use in crown force calculations.

The effective roll crown term ERC represents the average value of the diametral crown on the rolls in the mill. The diametral crown of a new roll is measured before installing the roll in the mill housing. Such crown measurements, in properly coded form are part of the mill data supplied to the computer 46 through the auxiliary input 50. The effective crown on the rolls in either the roughing or finishing mill varies after installation due to thermal expansion and wear, making it necessary to update the term ERC at regular intervals. Different methods are used to update the term ERC for the mill l0 and 24. The particular methods used are set out later in the descriptions of the specific problems in shape control encountered during the roughing and finishing phases.

An inspection of the crown-force equation shows that there are two crown components considered. The effect of plate width on the plate crown component (MH) (PCW) (TC) is established by the force multiplier PCW. The effects of plate width on the roll-crown component (RC W) (ERC) is established by the force multiplier RCW. Generally, the formation of a given crown on a narrow plate requires a much greater roll-separating force than the formation of the same crown on a relatively wider plate. The reasons for this are illustrated in part by reference to FIG. 2, consisting of FIGS. 2A and 28. FIG. 2A shows, in greatly exaggerated form, an upper work roll 52a deflected by a plate 54 to form a crown 56 on the upper surface of the plate having an edge gage 58. FIG. 2B shows a work roll 52b deflected into precisely the same shape as work roll 52a, but by a relatively wider plate 60 having an edge gage 62. Although the shapes of the rolls 52a and 5212 are identical, the crown 64 on the plate 60 is considerably larger than the crown 56 on the plate 54. The roll-separating force on the roll 520 must be greatly increased before that roll will deflect sufficiently to establish a crown on plate 54 equal to the crown 64 on the plate 60.

Consideration of FIG. 2 leads to the conclusion that there is an inverse relationship between plate width and the force multiplier PC W. FIG. 3 illustrates the relationship for both a twohigh mill such as mill l0 and a four-high mill such as mill 24. Although curve 66 relating width to the value of PCW in a four-high mill has the same general form as curve 68 relating width to the value of PC W in a two-high mill, curve 66 is displaced in a generally vertical direction from curve 68, indicating that greater roll-separating forces will be needed to form a given crown on a plate of given width in a four-high mill than in a two-high mill under the same conditions. The greater rollseparating forces in the four-high mill are made necessary by the greater cross-sectional moment of inertia of the rolls in that type of mill.

The work rolls in either a four-high or a two-high mill have a generally parabolic shape and are less effective in rolling narrow plates than wide ones. For this reason, the crown-force equation includes force multiplier RCW. FIG. 4 illustrates the relationship of plate width to the value of multiplier RC W for both a four-high mill (curve 70) and a two-high mill (curve 72). While the value of the multiplier RCW does vary with plate width to account for variations in roll effectiveness, the variations are slight compared to variations in the multiplier PCW. The appearance of FIG. 4 is deceptive at first glance. Note the force-multiplier scale of FIG. 4 is greatly expanded (00.50) relative to the force-multiplier scale of FIG. 3 (0-9.0). Despite physical appearances of curves in those figures, the FIG. 4 curves represent a force-multiplier range of 00.50+ while the FIG. 3 curves represent a force-multiplier range of 0 9.0 g

Generally, as a plate becomes thinner, its resistance to deformation during rolling increases. The variations in rollseparating forces needed to compensate for the changes in resistance to deformation are taken into account by the resistance to deformation multiplier MH. In establishing the value of the multiplier MH, plate-deformation curves such as the one shown in FIG. 5 may be used. Plate-deformation curves generally relate roll-separating forces to the reduction which may be expected in a workpiece having a particular entry gage, metallurgical composition, and temperature. It is possible and preferable in practicing the present invention to derive and store families of plate-deformation curves as functions of gage alone. In this case, the differences in deformation characteristics due to differences in metallurgical composition (grade code) and/or temperature are taken into account by separately stored multipliers. The base values for plate-deformation curves and the values for temperature and grade-code multipliers have been derived from metallurgical theory and verified by observation. Since such curves and multipliers are well known in the an, nothing further need be said concerning their derivation.

The first step in deriving the resistance to deformation multiplier MH for a particular pass requires that the incremental resistance to deformation be calculated for the expected draft. An estimate is made as to the draft which should be taken on the pass based upon known material density and predicted temperature at the beginning of the pass. The estimated draft should not be confused with the actual draft which later calculations may show is required during that pass. Referring to FIG. 5, the estimated draft may have a value D1. To calculate the incremental resistance to deformatiop in the region of the draft D1, drafts D2 and D3 lesser and greater than the estimated draft D1 are selected. In a preferred embodiment, the drafts D2 and D3 differ from the draft D1 by a fixed percentage. For example, the draft D2 may equal 0.98 D! while the draft D3 may equal l .02 D1. The roll-separating forces F2 and F3 needed to effect the drafts D2 and D3 respectively are derived from the plate-deformation curve of FIG. 5. The incremental resistance to deformation in the area of the draft D1 is then calculated as the ratio of the force differential to the draft differential or F3F2/D3-D2 which equals the slope of a straight line drawn between the intercepts of the drafts D2 and D3 with the plate deformation curve.

In deriving the resistance to deformation multiplier from the incremental resistance to deformation, the effective plate width is considered. FIG. 6 illustrates the relationship between the plate width and the resistance to deformation multiplier MH for certain values of incremental resistances to deformation. Reviewing this figure shows that the resistance to deformation multiplier MH ranges between approximately 0.5 and 5.0 for different deformation resistances at different plate widths. In most instances the actual width of the plate being rolled and the magnitude of the incremental resistance to deformation for that plate will not match exactly the magnitudes of coordinates stored by the computer 46. In such instances, the value of multiplier MH is obtained by interpolating linearly between the closest values of stored widths and deformation resistances.

The physical effects of different resistances to deformation during rolling are illustrated with reference to FIG. 9, consisting of FIGS. 9A and 98.

FIG. 9A shows vectors representing the distribution of rollseparating force during the reduction of an upper half of a soft" plate 94 by a work roll 96. The soft plate deforms freely to follow the contour of the work-roll surface, resulting in a relatively uniform force distribution, and a relatively uniform roll-surface deformation.

In contrast, FIG. 9B shows the force distribution across a har plate 98. For purposes of illustration, assume that the plate is infinitely hard and will not deform. Then the difference in roll axis deflection at points above the plates edge and center must exactly equal and oppose the plates edge and center must exactly equal and oppose the difference in rollsurface deformation at those points. The force distribution must be of the nature shown in FIG. 98 to produce this result. Thus, even though the total roll-separating forces may be the same for the soft plate 94 and the hard plate 98, the different force distribution results in the formation of a lower crown on the plate 98. The shift of force towards the roll bearings reduces roll bending and its contribution to plate crown. Also, the increased forces at the plate edges result in increased nonuniform deformation of the roll face particularly near the plate edges, thereby reducing plate-crown formation even more.

These effects of resistance to deformation on crown-force calculations were not considered by prior art systems even though experiences in practicing the present invention have shown that the forces needed to roll a particular crown on a plate of a particular width may vary over a two to one range due to differences in resistance to deformation.

The terms of the crown-force equation discussed so far are determined by the properties of the mill or plate. The one remaining term, the target-crown term TC, may be adjusted to accomplish the objective of shape control. Different methods are used to determine the value of the term TC depending on whether the plate is in the roughing phase or finishing phase. The particular methods used are set forth in the description of the specific problems of shape control encountered during the roughing and finishing phases.

During the roughing phase, the problem of shape control is not highly significant prior to the last pass which is taken for purposes of establishing the width of the finished plate. During this pass, however, it is desirable to provide shape control for purposes of pattern correction. In manual operations, the mill operator normally takes a small reduction on this last pass. The resulting low force and corresponding low mill stretch reduces the gage uncertainty and simplifies his task of controlling width. Usually this lower force will not bend the rolls sufficiently to offset the roll crown, particularly in two-high mills employing rolls with comparatively large crowns. The resulting negative plate crown will produce a slab having a convex-ended pattern such as that illustrated in FIG. 7. The objective of shape control as applied to such a slab during the last width-establishing pass is to eliminate or at least reduce the excessive center length by properly loading the mill rolls, to bring the slab pattern toward the ideal illustrated by the dotted lines in FIG. 7. Specific relationships between changes in formed crowns and changes in plate patterns have been derived by theory and verified by observation. These specific relationships are used to effect pattern correction through crown control during the last pass in the roughing phase.

In carrying out the crown control during pattern correction, the crown force equation discussed in general terms is modified. The fact that the slab has had relatively little time to cool and is still relatively thick during the roughing phase makes it unnecessary to consider crown-force multipliers due to resistance to deformation. For that reason, the multiplier MH is eliminated from the crown-force equation used during the roughing phase. The equation then takes the form:

The derivation of the terms RM, RD, PCW, and RCW have been discussed. Each of these terms may be calculated prior to the last pass during the roughing phase based on known data. Although the value of the term TC may initially be established at a base-crown value, it is this term which is modified as a function of the sensed pattern of earlier processed slabs to accomplish pattern correction during the last width-establishing pass of the slab presently being rolled.

In a preferred embodiment of the invention, it is necessary to distinguish between only three conditions of plate pattern. The first condition is a plate with an acceptable pattern which would be a rectangular or nearly rectangular plate. The second condition is a long center condition in which the plate is elongated more at its center than at its edges as illustrated in FIG. 7. The third condition is a short center condition in which the center of the plate is elongated less than its edges. Although an operator nonnally performs the function of distinguishing between these three pattern conditions, an apparatus such as that shown in FIG. 8 may be used for the same purpose. In FIG. 8, a slab 74 is shown emerging from between the rolls of the roughing mill, of which only roll 76 is shown, during the last width-establishing pass in the roughing phase. As the slab 74 moves along the mill table 78, the shape of one end of the slab is sensed by a set of scanners S1, S2, and S3 located above the edges and the center of the slab 74. The scanners, which may be of a conventional photoelectric or infrared variety, scan in synchronism along the direction of the mill table. The shape of the end of the slab determines which of the scanners detects the slab edge first. Although it is possible to determine the extent of pattern variation, the present invention requires only a determination whether the center of the finished slab is shorter or longer than the edges.

The object of shape control during the roughing phase is to set the spacing between the roll 76 and its associated lower work roll to produce a draft which will bend the rolls an amount equal to their crowns so as to produce a rectangular loaded roll gap as the slab passes back through the roughing mill during the last width-establishing pass. Where the mill had been producing slabs like the slab 74 shown in FIG. 8, the target crown TC would be increased by a fixed increment in response to the sensed patterns of the earlier processed slabs. Using the incremented term TC, the roll-separating force required to produce the incremented value TC is calculated by means of the crown-force equation. Because the target crown is increased, the roll-separating force for the last pass is also increased, reducing the elongation of the center of slab 74 relative to its edges during the last pass. The objective is a more nearly rectangular plate for use during the finishing phase.

The effective roll-crown term ERC used in the crown force equation during the roughing phase is initially based on the ground crown in the roughing mill rolls. There is, however, a definite relationship between the term ERC and the pattern of the plate as observed prior to the last pass in the roughing phase. For that reason, the term ERC is updated subsequent to the last pass in the roughing phase by an appropriate factor which either increases or decreases the value of the effective roll crown depending upon the type of pattern sensed.

If the mill rolls appear to be wearing rapidly or are subject to frequent and severe temperature variations, the updating procedure may be supplemented by separate computations for changes in roll crown due to roll thermal expansion or roll wear. Calculation of either thermal expansion or wear requires knowledge of the amount of time the rolls have been in contact with plates being reduced and the amount of time between rolling schedules and between individual passes within each rolling schedule. With this knowledge, as provided by the plate-tracking system 48, and knowledge as to the rate of heating and cooling of the rolls under various'thermal conditions, the thermal expansion of each roll may be calculated. The roll wear can be treated as a linear function of the plate tonnage rolled in the mill. In many instances, it may not be necessary to calculate roll thermal expansion or roll wear separately since their long range effects on roll crown are inherently compensated for in the updating procedure based on sensed pattern.

The problem of shape control during the finishing phase are more complex than those encountered during the roughing phase and require consideration of the deformation resistance of the material, the proper value of target crown for the last pass in the finishing phase, and the relationship between the per unit crowns formed on the earlier passes during the finishing phase.

In setting up a rolling schedule in a finishing mill, the first step is the determination of a target crown for the last pass in the rolling schedule. If a target crown is not established by specified overweight limits or by industry specifications, it may be calculated from stored rules. For example, the computer 46 may calculate a target crown which, recognizing the essentially parabolic form of the roll opening, is expressed as kW where k is a constant on the order of 0.0005 mils/in. and W represents the width of the plate in inches. For a plate 80 inches wide, the target crown using this formula would be 0.0005 or 3.2 mils. It is desirable to express the target crown in terms of plate width to avoid the use of excessive roll-separating forces which would be necessary to roll a fixed absolute target crown on a narrow plate. Other strategies can be used in establishing the relationship between the width and target crown. For example, a linear relation between target crown and width could be used. However, this is a less conservative practice than the practice first suggested.

When the target crown for the last pass (pass n) is determined along with the other terms of the crown-force equation, the equation is used to calculate the roll-separating force required during pass n to produce this target crown. Once the roll-separating force required on the last pass is known along with the desired gage following the pass, the entry gage for the last pass may be determined from known plate-deformation curves such as the one described in connection with FIG. 5. The next step in the generation of a rolling schedule for the finishing mill is the determination of a target crown for the next to the last pass or pass nl. Rather than complicate the discussion of the basic schedule generation process, the description of techniques by which target crowns are established for each pass is deferred until later. Once a suitable crown (C,, is established for pass nl the roll-separating force F,, is calculated using the crown-force equation. Again, knowing the gage-following pass n1 and the rollseparating fore F the gage at the entry to pass n-] (the exit of pass n2 may be derived from plate-deformation curves.

From the preceding discussion, it may be seen that the generation of the rolling schedule for the finishing phase requires that a certain sequence of calculations be repeated for each pass in the rolling schedule. Each sequence of calculations involves the following steps:

1. Determination of the target crown for the pass according to stored rules or techniques discussed below.

2. Determination of the roll-separating forces required to form the target crown by use of the crown-force equation.

3. Determination of the entry gage to the pass from the known delivery gage, the calculated roll-separating forces, and the known plate-deformation curves.

The calculations outlined above are repeated for successively earlier passes until the calculated entry gage of the plate for one of the passes is equal to or greater than the actual entry gage of the plate at the beginning of the rolling schedule. If the calculated entry gage exceeds the actual entry gage, a rounding-off procedure is employed to match the calculated entry gage with the actual entry gage. The rounding-off procedure is known and need not be described here. Of course, during the generation of the rolling schedule, operating limits such as allowable force or motor torque must not be exceeded. If an operating limit would be exceeded by a planned draft, the draft may be limited to the maximum or minimum value consistent with the operating limit and/or the mill operator may be altered by a suitable alarm which would permit him to assume manual control of the mill.

When an acceptable rolling schedule has been generated, the roll opening for the first pass is calculated based upon the desired draft, the plate dimensions, the metallurgy and temperature, and the mill-deformation characteristics. Roll openings are calculated for each subsequent pass only after analysis of data obtained during the preceding pass so that unexplained variations in resistance to deformation may be accounted for.

That the mill stretch must be considered in establishing the roll openings for each pass in a rolling schedule is widely known. The stretch of a plate mill as a function of force may be described as a family of curves varying from one another as a function of the width of plates being processed in the mill. According to the prior art, the stretch for a plate at a given width could be determined by the intercept of the appropriate stretch curve with the force level line corresponding to the force to be expected during the pass.

The key to controlling shape during the finishing phase is maintaining a predetermined relationship between plate crowns formed on successive passes during the finishing phase. In establishing the relationship, use is made of a multiplier referred to as a crown-slope multiplier (CSM), having a magnitude equal to or greater than one. In a preferred embodiment of the invention, these crown-slope multipliers are stored in memory units for computer 46 as a function of final gage-range, final plate width, and plate grade-code. The CSM is a measure of the change in per unit crown which can be tolerated for successive passes in a rolling schedule for various plate dimensions and grade codes. Modifications to the resistance to deformation multiplier MH for finishing passes prior to the last pass, to account for changes in plate temperature are incorporated into the CSM. Theoretical optimums for the CSM are known and deviations from values allowing ideal plate shape are allowed only when the number of finishing passes may be modified for production reasons without degrading final plate shape.

The use of the crown slope multiplier in establishing the proper target crowns for passes prior to the last pass in the finishing phase is explained with reference to FIG. 10. That figure shows the cross-sectional view of a plate on three successive passes with the plate crowns greatly exaggerated for purposes of clarity. The final plate gage H,, is established prior to the generation of a rolling schedule by customer specification. The final plate crown equals C,,, which is established by customer or industry specification or stored rules. In using the crown slope multiplier to determine the proper target crowns in passes prior to the final (pass n), the per unit crown for pass n (p.u. C is calculated as the ratio of the crown following pass n to the gage following pass n or C,,H,,. The per unit crown (p.u. C for pass nl is established as CSMXp.u. C,,. However, the crown-force equation does not include per unit crown as one of its terms but rather absolute crown. For this reason, it is necessary to convert p.u. C to an absolute crown value before using the crown force equation to determine the roll-separating force needed on pass nl to form crown C,, Referring back to pass n, after the roll-separating force for pass n has been calculated using the crown force equation, the delivery gage H,, for pass nl may be determined from plate-deformation curves such as the one shown in FIG. 5. Knowing both H,, and p.u. C,, the absolute crown C,, may be determined as the product of these quantities. With both the absolute crown and the delivery gage known for pass nl, the roll-separating force needed during that pass may be calculated by the crown-force equation.

The per unit crown (p.u. C,, for pass n2 is the product of the crown-slope multiplier and the per unit crown for pass nl or CSMXp.u. C,, In determining the absolute crown for pass PUP.

n-2, the gage H is determined by use of the force needed on pass 11-1 and plate-deformation curves in the same way as was done for pass n-l.

The procedure described above is repeated for successively earlier passes until a target crown for each pass in the rolling schedule has been generated. Because the per unit crown for a particular pass is always determined as the product of the crown slope multiplier CSM and the per unit crown for the next succeeding pass, the formula for the per unit crown on a pass n-y may be written as (CSM)" p.u. C,,. Of course, it is possible that the increasing crowns will require greater and greater roll-separating forces until a maximum allowable force is reached. if the maximum allowable force is reached before the complete rolling schedule is generated, the roll-separating forces for all earlier passes are maintained at a constant value equal to the maximum value.

Referring to FIG. 1 1, the curve of the per unit crown on successive passes follows a generally parabolic form as would be expected from the equation by which those per unit crowns are calculated. it should be noted that, according to the present invention, the changes in absolute crown on the last few passes in the rolling schedule are much smaller than the changes in absolute crown during the earlier passes. The greater absolute crowns are acceptable on the earlier passes during the rolling schedule since the plate is still relatively thick during those earlier passes and thus able to accommodate greater changes in crown without distortion.

The crown slope multipliers may be considered base values which are subject to modification in response to observations of the flatness of finished plates. As indicated earlier, the flatness of a finished plate is normally and preferably judged by the mill operator. However, it is possible to devise a flatness sensor capable of distinguishing between three significant conditions of flatness: perfect flatness, wavy edges, and center buckle. FIG. 12 is a plan view of one embodiment of a flatness monitor. in that figure, a finished plate 80 is depicted as moving along a mill table 82 between rolls in a finishing mill, of which only a single work roll 84 is shown. As the plate 80 emerges from the mill, it passes beneath a pair of optical or acoustical sensors 86 and 88 located above the center and edge of the plate 80. Referring to FIG. 13, each of these sensors includes a radiation source 90 for producing a beam of optical or acoustical radiation which is directed toward the surface of the moving plate- The reflected radiation is detected by a receiving unit 92 spaced along the mill table 82. if the plate is flat (neither buckled nor wavy), the reflected radiation will remain at a relatively constant level. However, if the area below the units is buckled or wavy, the reflected radiation will fluctuate due to the constantly changing angle of reflection from the distorted plate surfaces.

The performance of the illustrated device and of a mill operator are essentially the same. if the finished plate is flat, the operator takes no action. If the edges of the plate are wavy, the operator submits a coded wavy edge input to the computer 46 which results in the generation of a +1 count in computer 46. If the center area of the plate is buckled, the operator submits a coded center buckle" input which results in the generation of a 1 count. The counts are added algebraically in an accumulator, multiplied by a gain term, and added to the base values of the crown slope multiplier stored in the memory units for the computer 46. Experience indicates that a gain of between 0.05 and 0. l is appropriate for each input supplied by the operator. The accumulated count is reset whenever the rolls in the finishing mill are changed.

It is possible to modify the stored crown-slope multiplier base values automatically as a function of the operators submitted observations. Experience indicates, however, that once the system has been adjusted, distorted plates are the result of the current condition of the mill rolls or significant changes in incoming plate temperature. Thus the modifiers are best treated as temporary while the base values for the crown-slope multipliers are held intact.

The value of the effective roll crown is updated in the finishing mill at the completion of each rolling schedule between roll changes. Upon mathematically rearranging the crown force equation,

Using the final pass roll-separating force measured by load cell 40 in FIG. l and the final crown determined from the center and edge thicknesses measured by gage 42 as the values for F and TC in the rearranged equation and holding the remaining terms at the values used in the earlier calculations of rollseparating force, the measured effective roll crown is calculated. The difference between the measured effective roll crown and the roll crown used during earlier calculations determines the magnitude of a gain factor applied to the old effective roll-crown value. A gain factor is used in preference to merely adopting the measured effective roll crown since the reliability and calibration of the thickness gages are sometimes subject to doubt. The magnitude of the gain factor is, for this reason, made inversely proportional to the difference between the measured crown and the old crown. That is, for larger crown differences, the gain factor is relatively smaller, varying by a ratio of as much as 10 to I over the complete range of crown differences.

If the work rolls appear to be wearing rapidly or are subject to frequent and severe temperature variations, the effective roll crown updating procedure for the finishing mill may also include separate computations for changes in roll crown due to roll thermal expansion or roll wear. These calculations are described with reference to the roughing mill. Just as in the roughing mill, it may not be necessary to calculate roll thermal expansion or roll wear separately in the finishing mill since their long range effects on roll crown are inherently compensated for in the updating calculations of effective roll crown using measured plate crown and measured force values.

We claim:

1. For use in a rolling mill having at least one pair of opposed rolls in a mill housing, a method of controlling the shape of a plate including the steps of:

a. determining an incremental deformation characteristic for the plate to be rolled from the slope of a functiondefining rolling force against plate deformation at approximately the deformation anticipated during rolling;

b. accessing selected functions of resistance to deformation against plate width for the determined incremental deformation characteristic to obtain the resistance to deformation for said plate;

c. determining the roll-separating force required on the last rolling pass of the plate between the opposed rolls to form a predetermined crown as a function of the modulus of elasticity of the opposed rolls, the diameters of the opposed rolls, the resistance to deformation of the plate, the width of the plate, and the effective crown on the opposed rolls;

d. predicting the mill stretch as a function of the rollseparating force required on the last rolling pass and the width of the plate;

e. positioning the rolls to provide a roll opening equal to the gage desired for the plate minus the mill stretch predicted for the last rolling pass; and

f. passing the plate between the opposed rolls.

2. A method of controlling the shape of a plate as recited in claim 1 wherein the roll-separating force f required on the last rolling pass is determined by a crown force equation having the form F=(RM)-(RD)-[(MH)'(PCW)-(TC)+(RCW)-(ERC)] wherein RM is proportional to the modulus of elasticity of the opposed rolls, RD is proportional to the diameters of the opposed rolls, MH is proportional to the resistance to deformation of the plate, PCW is proportional to the width of the plate, TC is proportional to the target crown for the plate, RCW is proportional to the width of the plate, and ERC is proportional to the effective crown on the opposed rolls.

3. For use in a rolling mill having at least one pair of opposed rolls in a mill housing, a method of controlling the shape of a plate when the final gage and crown are specified, including the steps of:

a. establishing a target per unit crown on the plate for each rolling pass beginning with the specified final per unit crown by multiplying each previously established per unit crown by a crown slope multiplier having a magnitude greater than one, whereby successively greater per unit crowns are established for successively earlier rolling passes;

b. determining the roll-separating force required to produce a target crown on the plate on each rolling pass as a function of the effective roll crown, the modulus of elasticity of the opposed rolls, the diameters of the opposed rolls, and the resistance to deformation, the width, the per unit crown, and the delivery gage of the plate;

c. determining the entry gage for each rolling pass beginning with the last rolling pass as a function of the roll-separating force required on that pass, the desired delivery gage, and the plate-deformation characteristics;

d. predicting the stretch of the mill on each rolling pass as a function of the determined roll-separating force and the plate width;

e. changing the roll openings for successively later passes as a function of the predicted stretch of the mill and of the desired delivery gage for each particular pass; and

f. passing the plate between the opposed rolls following each change in the roll opening.

4. A method of controlling the shape of a workpiece as recited in claim 3 wherein the roll-separating force F required to produce the target crown on the workpiece on each rolling pass is determined by use of the crown force equation F=(RM)-(RD)-[(MH)-(PCW)-( TC)+(RCW)-(ERC)] whereas RM is proportional to the modulus of elasticity of the opposed rolls, RD is proportional to the diameters of the opposed rolls, MH is proportional to the resistance to deformation of the plate, PC W is proportional to the width of the plate, TC is proportional to the target crown for the plate, RCW is proportional to the width of the plate, and ERC is proportional to the effective crown on the opposed rolls.

5. A method of controlling the shape of a plate as recited in claim 3 including the steps of:

a. establishing a plurality of values for the crown-slope multiplier as functions of the width, final desired gage and grade code of the plate; and

b. altering each of the plurality of values in a predetermined manner in response to encoded observations of the shapes of previously rolled plates.

6. A method of controlling the shape of a plate as recited in claim 4 including the steps of:

a. establishing a plurality of values for a crown-slope multiplier as functions of the width, final desired gage and grade code of the plate; and

b. altering each of the plurality of values in a predetermined manner in response to encoded observations of the shapes of previously rolled plates.

7. A method of rolling slab in a roughing mill wherein the slab is multiply passed between at least one pair of opposed roughing rolls to elongate the slab in a direction perpendicular to the axes of said rolls prior to finish rolling wherein the slab is rolled in a direction generally orthogonal to the direction of rolling in the roughing mill, the method comprising:

a. detecting the position of a slab edge disposed substantially parallel to the axes of said roughing rolls at diverse spans from the longitudinal centerline of the roughing mill,

b. comparing the detected positions of said slab edge at said diverse spans to provide a signal corresponding to the variation in the shape of said edge relative to the axes of said roughing rolls, and

c. adjusting the magnitude of the crown to be rolled on slab during the last pass of the slab through the roughing mill as a function of the detected shape of the edge relative to the axes of the roughing rolls.

8. A method of rolling slab as recited in claim 7 including the further steps of:

a. determining the roll-separating force required to produce a rectangular roll gap during the last width-establishing pass of a particular slab as a function of the adjusted roll crown, the modulus of elasticity of the opposed rolls, the diameters of the opposed rolls, and the width of the slab;

b. predicting the mill stretch during the last width-establishing pass as a function of the determined roll-separating force and the slab width;

c. positioning the rolls to provide an unloaded roll opening equal to the desired final gage minus the predicted stretch; and

d. passing the slab between the positioned rolls.

9. A method of rolling slab as recited in claim 8 wherein the roll-separating force F required on the last width-establishing pass is determined by a crown force equation having the form F=(RM)-(RD)-[(PCW)-(TCH-(RCWHERCH wherein RM is proportional to the modulus of elasticity of the opposed rolls, RD is proportional to the diameters of the opposed rolls, PCW and RCW are proportional to the width of the plate, TC is proportional to the target crown for the plate and ERC is proportional to the effective crown on the opposed rolls. 

1. For use in a rolling mill having at least one pair of opposed rolls in a mill housing, a method of controlling the shape of a plate including the steps of: a. determining an incremental deformation characteristic for the plate to be rolled from the slope of a function-defining rolling force against plate deformation at approximately the deformation anticipated during rolling; b. accessing selected functions of resistance to deformation against plate width for the determined incremental deformation characteristic to obtain the resistance to deformation for said plate; c. determining the roll-separating force required on the last rolling pass of the plate between the opposed rolls to form a predetermined crown as a function of the modulus of elasticity of the opposed rolls, the diameters of the opposed rolls, the resistance to deformation of the plate, the width of the plate, and the effective crown on the opposed rolls; d. predicting the mill stretch as a function of the rollseparating force required on the last rolling pass and the width of the plate; e. positioning the rolls to provide a roll opening equal to the gage desired for the plate minus the mill stretch predicted for the last rolling pass; and f. passing the plate between the opposed rolls.
 2. A method of controlling the shape of a plate as recited in claim 1 wherein the roll-separating force f required on the last rolling pass is determined by a crown force equation having the form F (RM).(RD).((MH).(PCW).(TC)+(RCW).(ERC)) wherein RM is proportional to the modulus of elasticity of the opposed rolls, RD is proportional to the diameters of the opposed rolls, MH is proportional to the resistance to deformation of the plate, PCW is proportional to the width of the plate, TC is proportional to the target crown for the plate, RCW is proportional to the width of the plate, and ERC is proportional to the effective crown on the opposed rolls.
 3. For use in a rolling mill having at least one pair of opposed rolls in a mill housing, a method of controlling the shape of a plate when the final gage and crown are specified, including the steps of: a. establishing a target per unit crown on the plate for each rolling pass beginning with the specified final per unit crown by multiplying each previously established per unit crown by a crown slope multiplier having a magnitude greater than one, whereby successively greater per unit crowns are established for successively earlier rolling passes; b. determining the roll-separating force required to produce a target crown on the plate on each rolling pass as a function of the effective roll crown, the modulus of elasticity of the opposed rolls, the diameters of the opposed rolls, and the resistance to deformation, the width, the per unit crown, and the delivery gage of the plate; c. determining the entry gage for each rolling pass beginning with the last rolling pass as a function of the roll-separating force required on that pass, the desired delivery gage, and the plate-deformation characteristics; d. predicting the stretch of the mill on each rolling pass as a function of the determined roll-separating force and the plate width; e. changing the roll openings for successively later passes as a function of the predicted stretch of the mill and of the desired delivery gage for each particular pass; and f. passing the plate between the opposed rolls following each change in the roll opening.
 4. A method of controlling the shape of a workpiece as recited in claim 3 wherein the roll-separating force F required to produce the target crown on the workpiece on each rolling pass is determined by use of the crown force equation F (RM).(RD).((MH).(PCW).(TC)+(RCW).(ERC)) whereas RM is proportional to the modulus of elasticity of the opposed rolls, RD is proportional to the diameters of the opposed rolls, MH is proportional to the resistance to deformation of the plate, PCW is proportional to the width of the plate, TC is proportional to the target crown for the plate, RCW is proportional to the width of the plate, and ERC is proportional to the effective crown on the opposed rolls.
 5. A method of controlling the shape of a plate as recited in claim 3 including the steps of: a. establishing a plurality of values for the crown-slope multiplier as functions of the width, final desired gage and grade code of the plate; and b. altering each of the plurality of values in a predetermined manner in response to encoded observations of the shapes of previously rolled plates.
 6. A method of controlling the shape of a plate as recited in claim 4 including the steps of: a. establishing a plurality of values for a crown-slope multiplier as functions of the width, final desired gage and grade code of the plate; and b. altering each of the plurality of values in a predetermined manner in response to encoded observations of the shapes of previously rolled plates.
 7. A method of rolling slab in a roughing mill wherein the slab is multiply passed between at least one pair of opposed roughing rolls to elongate the slab in a direction perpendicular to the axes of said rolls prior to finish rolling wherein the slab is rolled in a direction generally orthogonal to the direction of rolling in the roughing mill, the method comprising: a. detecting the position of a slab edge disposed substantially parallel to the axes of said roughing rolls at diverse spans from the longitudinal centerline of the roughing mill, b. comparing the detected positions of said slab edge at said diverse spans to provide a signal corresponding to the variation in the shape of said edge relative to the axes of said roughing rolls, and c. adjusting the magnitude of the crown to be rolled on slab during the last pass of the slab through the roughing mill as a function of the detected shape of the edge relative to the axes of the roughing rolls.
 8. A method of rolling slab as recited in claim 7 including the further steps of: a. determining the roll-separating force required to produce a rectangular roll gap during the last width-establishing pass of a particular slab as a function of the adjusted roll crown, the modulus of elasticity of the opposed rolls, the diameters of the opposed rolls, and the width of the slab; b. predicting the mill stretch during the last width-establishing pass as a function of the determined roll-separating force and the slab width; c. positioning the rolls to provide an unloaded roll opening equal to the desired final gage minus the predicted stretch; and d. passing the slab between the positioned rolls.
 9. A method of rolling slab as recited in claim 8 wherein the roll-separating force F required on the last width-establishing pass is determined by a crown force equation having the form F (RM).(RD).((PCW).(TC)+(RCW).(ERC)) wherein RM is proportional to the modulus of elasticity of the opposed rolls, RD is proportional to the diameters of the opposed rolls, PCW and RCW are proportional to the width of the plate, TC is proportional to the target crown for the plate and ERC is proportional to the effective crown on the opposed rolls. 